Permutations an...

The total number of five digit numbers the sum of whose digits is even is 

If $$^{40}C_{n+7} = ^{40}C_{4n-2},$$ then all the values of n are given by

If, $$\dfrac{1}{^5C_r}+\dfrac{1}{^6C_r} = \dfrac{1}{^4C_r}$$, then the value of $$r$$ equals to

Ten different letters of alphabet are given, words with five letters are formed with these given letters. Then the number of words which have at least one letter repeated

When listing the integers from $$1$$ to $$1000$$, how many times the digit $$5$$ be written?

If $$^nC_8 = ^nC_{27}$$, then what is the value of $$n?$$

The exponent of $$18$$ in $$200!$$, is

Find the number of subsets of the set $${1,2,3,4,5,6,7,8,9,10,11}$$ having $$4$$ elements

There are $$8$$ true/false questions in an examination.The number of ways in which this questions can be answered, is

There are $$8$$ men and $$10$$ women and you need to form a committee of $$5$$ men and $$6$$ women. In how many ways can the committee be formed?